QuestionFind the probability of Michael Phelps choosing each type of medal: gold, silver, and bronze, given he has 23 gold, 3 silver, and 2 bronze.

Studdy Solution

STEP 1

Assumptions1. Michael Phelps has won23 gold medals. Michael Phelps has won3 silver medals3. Michael Phelps has won bronze medals4. He chooses a medal at random

STEP 2

First, we need to find the total number of medals won by Michael Phelps. We can do this by adding the number of gold, silver, and bronze medals.
$Total\, medals = Gold\, medals + Silver\, medals + Bronze\, medals$

STEP 3

Now, plug in the given values for the number of gold, silver, and bronze medals to calculate the total number of medals.
$Total\, medals =23 +3 +2$

STEP 4

Calculate the total number of medals won by Michael Phelps.
$Total\, medals =23 +3 +2 =28$

STEP 5

The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the favorable outcomes are the number of each type of medal, and the total outcomes are the total number of medals. $Probability = \frac{Number\, of\, favorable\, outcomes}{Total\, number\, of\, outcomes}$

STEP 6

To find the probability of choosing a gold medal, plug in the number of gold medals for the number of favorable outcomes and the total number of medals for the total number of outcomes.
$Probability\, of\, gold = \frac{23}{28}$

STEP 7

To find the probability of choosing a silver medal, plug in the number of silver medals for the number of favorable outcomes and the total number of medals for the total number of outcomes.
$Probability\, of\, silver = \frac{3}{28}$

STEP 8

To find the probability of choosing a bronze medal, plug in the number of bronze medals for the number of favorable outcomes and the total number of medals for the total number of outcomes.
$Probability\, of\, bronze = \frac{2}{28}$ The probabilities are as follows1. The probability of choosing a gold medal is $\frac{23}{28}$
2. The probability of choosing a silver medal is $\frac{3}{28}$
3. The probability of choosing a bronze medal is $\frac{2}{28}$

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